Fault Diagnosis of Rolling Bearings using Multifractal Detrended Fluctuation Analysis and Mahalanobis Distance Criterion

Vibrations of a defective rolling bearing often
exhibit nonstationary and nonlinear characteristics which are
submerged in strong noise and interference components. Thus,
diagnostic feature extraction is always a challenge and has
aroused wide concerns for a long time. In this paper, the
multifractal detrended fluctuation analysis (MF-DFA) is
applied to uncover the multifractality buried in nonstationary
time series for exploring rolling bearing fault data.
Subsequently, a new approach for fault diagnosis is proposed
based on MF-DFA and Mahalanobis distance criterion. The
multifractality of bearing data is estimated with the
generalized Hurst exponent and the multifractal spectrum.
Five characteristic parameters which are sensitive to changes
of bearing fault conditions are extracted from the spectrum
for diagnosis of fault sizes. For benchmarking this new
method, the empirical mode decomposition (EMD) method is
also employed to analyze the same dataset. The results show
that MF-DFA outperforms EMD in revealing the nature of
rolling bearing fault data.